Method and system for measuring imbalances in an electrical grid

ABSTRACT

The invention relates to a method and a system for measuring imbalances in an electrical grid. The method comprises the steps of obtaining effective values and arguments of the phase voltages and currents at the fundamental frequency; calculating the effective value and the argument of the positive sequence voltages and the effective values of the negative sequence voltages; determining the active and reactive powers of each of the phases at the fundamental frequency; and calculating the value of the imbalance power vector according to the following equation: 
     
       
         
           
             
               
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     wherein a=1∠120°; j is the imaginary unit; δ U =V − /V +  and δ A =V 0 /V +  are the degrees of imbalance and asymmetry, respectively, of the phase voltages; and  p ,  q ,  z  are the orthogonal unit vectors defining the space itself of the imbalance power vector.

TECHNICAL FIELD OF THE INVENTION

The present invention generally relates to the field of the control andmaintenance of electrical grids and systems, and more specifically tomeasuring the energetic effects of voltage imbalances on the operationof three- and four-wire three-phase electrical systems, with balancedand unbalanced receivers.

PRIOR ART

Different formulations are known in the prior art for imbalance power,which is the magnitude in charge of measuring the effects of imbalanceson electrical systems (see, for example, L. S. Czarnecki, “Power relatedphenomena in three-phase unbalanced systems”, IEEE Trans on PowerDelivery, vol. 10, no. 3, July 1995; A. E. Emanuel, “TheBuchholz-Goodhue Apparent Power definition: The practical approach fornon-sinusoidal and unbalanced systems”, IEEE Trans on Power Delivery,vol. 13, no. 2, April 1998). A much-used expression of the imbalancepower (S_(u),) is the following, included in the draft for IEEE standard1459-2010, of the Institute of Electrical and Electronic Engineers ofthe United States of America, depending on the apparent power at thefundamental frequency (S₁) and the positive-sequence apparent power(S₊):

S _(u)=√{square root over (S ₁ ² −S ₊ ²)}

wherein the expressions of these apparent powers are:

S ₁=3√{square root over ((V ₊ ² +V ⁻ ² +V ₀ ²)·(I ₊ ² +I ⁻ ² +I ₀ ²))}

S ₊=3V ₊ I ₊

wherein the subscripts +, − and 0 respectively refer to positive(direct), negative (inverse) and zero (homopolar) sequence components ofthe phase voltages and currents of the system.

The preceding expressions of apparent powers are preferred in that theyare more closely related to the physical phenomena present in electricalsystems, in that the voltages and currents therein verify theKirchhoff's laws, and in that the first of the apparent powers providesthe same results as Buchholz's apparent power (1922). Therefore, theeffects of imbalances, measured by power S_(u), thereby obtained, areunderstood to be closer to what the phenomenon is actually like thanthose effects that are deduced from the use of other expressions ofapparent power with more mathematical significance are.

However, the use of power S_(u) to measure the effects of imbalances onelectrical systems is very limited, since this magnitude is notconservative, and therefore, the total imbalance power of an electricalinstallation or grid is not obtained as the sum of the imbalance powersof each of its receivers. Likewise, S_(u) does not provide informationabout whether the imbalance is due to resistive or reactive loads, or inwhich phase or phases the imbalances are more significant.

To avoid this drawback of S_(u), Spanish patent ES 2 316 280 B1,belonging to the same inventors as the present document, discloses amethod and system for measuring the so-called “imbalance power phasor”(Ā_(u)), a term that was used for the first time in said patent. Themodulus of the imbalance power phasor coincides with the value of S_(u)when system voltages are balanced. The imbalance power phasor is usefulfor measuring the effects of load imbalances and prevents some of theproblems with imbalance power S_(u). Depending on the active andreactive powers (P_(a), Q _(z)) of each phase of the system (z=1, 2, 3),the imbalance power phasor is expressed as follows:

Ā _(u)=√{square root over (2)}·(|P ₁ ^(b) +a ² P ₂ ^(b) +aP ₃ ^(b)|·p+|Q ₁ ^(b) +a ² Q ₂ ^(b) +aQ ₃ ^(b) |·q )

wherein a=1∠120°; p, q are the orthogonal coordinate axes defining theplane where the imbalance power phasor is represented and superscript bdenotes that said powers correspond to balanced voltages.

Therefore, the imbalance power phasor presents certain advantages withrespect to S_(u). However, it does not measure the effects caused byvoltage imbalances; therefore, use thereof is limited to the analysis ofimbalances produced by electrical loads when supply voltages areperfectly balanced or have very minor imbalances.

From the energy viewpoint, voltage imbalances in electrical systemsintervene in two ways: on one hand, they disturb the power flows broughtabout by load imbalances;

and on the other hand, give rise to a power flow characteristic of thevoltage imbalance, which is defined in a dimension other than the planeof the load imbalance. In other words, the complete measurement of theenergetic effects of imbalances on electrical systems requires a vectormagnitude, represented in a three-dimensional space (p, q, z).

Therefore, there continues to be a need in the art for a method andsystem that allow measuring imbalances in an electrical grid due to botheffects of load imbalances and effects of voltage imbalances.

BRIEF DISCLOSURE OF THE INVENTION

According to a first aspect, the present invention discloses a methodfor measuring imbalances in an electrical grid comprising the steps of:

-   i) obtaining effective values (V_(A1), V_(B1), V_(C1)) and arguments    (α_(A1), α_(B1), α_(C1)) of the phase voltages at the fundamental    frequency, as well as effective values (I_(A1), I_(B1), I_(C1)) and    arguments (β_(A1), β_(B1), β_(C1)) of the phase currents at the    fundamental frequency of the electrical grid;-   ii) calculating the effective value (V₊=V_(A1+)) and the argument    (α₊=α_(A1+)) of the positive sequence voltages and the effective    values of the negative sequence voltage (V⁻=V_(A1−)) and zero    sequence voltage (V₀=V_(A10));-   iii) determining the active power (P_(A1), P_(B1), P_(C1)) and    reactive power (Q _(A1), Q _(B1), Q _(C1)) of each of the phases at    the fundamental frequency from the values of the voltages and    currents at the fundamental frequency; and-   iv) calculating the value of the imbalance power vector (S _(u))    according to the following equation:

${\overset{\_}{S}}_{u} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{1}} \right)} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$$V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)++}}$$V_{+}{\sqrt{\delta_{u}^{2} + \; \delta_{A}^{2}} \cdot {{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}$

whereina=1∠120°;j is the imaginary unit;δ_(U)=V⁻/V₊ and δ_(A)=V₀/V₊ are the degrees of imbalance and asymmetry,respectively, of the phase voltages; andp, q, z are the orthogonal unit vectors defining the space itself of theimbalance power vector.

According to a second aspect, the present invention also discloses asystem for measuring imbalances in an electrical grid, comprising:

-   -   an analysis module, configured for obtaining effective values        (V_(A1), V_(B1), V_(C1)) and arguments (α_(A1), α_(B1), α_(C1))        of the phase voltages at the fundamental frequency, as well as        effective values (I_(A1), I_(B1), I_(C1)) and arguments (β_(A1),        β_(B1), β_(C1)) of the phase currents at the fundamental        frequency of the electrical grid;    -   a symmetrical module, configured for obtaining the effective        value (V₊=V_(A1+)) and the argument (α₊=α_(A1+)) of the positive        sequence voltages and the effective values of the negative        sequence voltage (V⁻=V_(A1−)) and zero sequence voltage        (V₀=V_(A10));    -   an active and reactive power module, configured for obtaining        the active power (P_(A1), P_(B1), P_(C1)) and reactive power (Q        _(A1), Q _(B1), Q _(C1)) of each of the phases at the        fundamental frequency;    -   an imbalance power vector module, configured for calculating the        value of the imbalance power vector (S _(u)) according to the        following equation:

${\overset{\_}{S}}_{u} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{1}} \right)} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$$V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)++}}$$V_{+}{\sqrt{\delta_{u}^{2} + \; \delta_{A}^{2}} \cdot {{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}$

whereina=1∠120°;j is the imaginary unit;δ_(U)=V⁻/V₊ and δ_(A)=V₀/V₊ are the degrees of imbalance and asymmetry,respectively, of the phase voltages; andp, q, z are the orthogonal unit vectors defining the space itself of theimbalance power vector; and

-   -   an information module, configured for providing information        about the calculated value of the imbalance power vector.

Therefore, the present invention provides a method and system formeasuring imbalances in an electrical grid, based on the calculation ofa new magnitude referred to as “imbalance power vector,” as will bedefined herein below. The imbalance power vector provides informationabout imbalances produced in an electrical grid due to effects of bothload and voltage imbalances that is more precise than what was madeavailable up until now in the prior art.

As a result of the information provided by means of the imbalance powervector, the method and system of the present invention will be veryuseful in a wide range of specific applications, such as for examplemeasuring instruments, protection instruments, machine regulatingequipment, active filters, electric machine maintenance, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood in reference to thefollowing drawings illustrating preferred embodiments of the invention,provided by way of example, and not to be interpreted as limiting theinvention in any way.

FIG. 1 is a diagram that graphically depicts the imbalance power vectorand its components in the space defined by the coordinate axes (p, q,z).

FIG. 2 is a block diagram depicting the imbalance power vector and therelationship with its different components.

FIG. 3 is a block diagram showing the operational sequence of a methodaccording to the preferred embodiment of the present invention.

FIG. 4 schematically shows a system for measuring according to thepreferred embodiment of the present invention.

FIG. 5 schematically shows an electrical circuit by way of example inwhich the system for measuring according to the preferred embodiment ofthe present invention is applied.

DETAILED DISCLOSURE OF PREFERRED EMBODIMENTS

The method and system for measuring disclosed in the present inventionare based on the calculation of a magnitude herein referred to as“imbalance power vector” (S _(u)). It is of a vector magnitude, i.e., itis defined in a three-dimensional space and has modulus, direction andsense. The modulus is always equal to the value of the imbalance powerS_(u), in systems with both balanced voltages and unbalanced voltages.

FIGS. 1 and 2 depict a graphic representation and block diagramrepresentation, respectively, of the imbalance power vector and therelationships with its various components.

From the viewpoint of practical usefulness, two main components of theimbalance power vector: S _(ui) and S _(uv), are distinguished first.The first component, S _(ui), measures the exclusive effects of loadimbalances (S _(ui) ^(b)) together with the effects originated thereonby voltage imbalances (S _(uiv)); this component of the imbalance powervector is represented in the plane defined by coordinate axes p, q.Therefore, plane (p, q) constitutes the joint domain of load and voltageimbalances. The second component, S _(uv), of the imbalance power vectordetermines the exclusive effect of voltage imbalances and is representedon axis z (domain of voltage imbalances), orthogonal to plane (p, q).

It must be noted that the component S _(ui) ^(b) coincides with theimbalance power phasor (Ā_(u)) of the prior art, a magnitude whichmeasures the exclusive effects of load imbalances, given thatsuperscript b indicates that voltages are balanced and therefore thereis no effect of voltage imbalance.

Finally, vector S _(uvT), the vector sum of S _(uiv) and S _(uv),defines the total effect of voltage imbalances on the electrical gridbeing studied.

The imbalance power vector and its components allow obtaining qualityfactors offering information about the effects of imbalances onelectrical grids, assessing the exclusive load imbalance or theexclusive voltage imbalance with respect to the total imbalance of thesystem, as well as the relative importance of resistive and reactiveload imbalances, among others.

Likewise, the total imbalance power in an electrical system or grid canbe obtained as the modulus of the vector resulting from the vector sumof the imbalance power vectors of each of the integrating parts thereof.

Now turning to FIG. 3, a block diagram depicting a method according tothe preferred embodiment of the present invention is shown, comprisingthe steps of:

Step (1): Digitally processing sampled signals obtained by means of aphysical system for measuring and acquiring electrical signals, thematrices of effective values (V_(A1), V_(B1), V_(C1)) and arguments(α_(A1), α_(B1), α_(C1)) of the voltage at the fundamental frequency foreach phase, as well as the matrices of effective values (I_(A1), I_(B1),I_(C1)) and arguments (β_(A1), β_(B1), β_(C1)) of the current at thefundamental frequency for each phase thereby being obtained.

-   -   Step (2): The symmetrical components, i.e., the effective value        (V₊=V_(A1+)) and the argument (α₊=α_(A1+)) of the positive        sequence voltages and the effective values of the negative        sequence voltage (V⁻=V_(A1−)) and zero sequence voltage        (V₀=V_(A10)) are obtained from the matrices obtained in step        (1).    -   Step (3): In parallel to step (2), the active power (P_(A1),        P_(B1), P_(C1)) and reactive power (Q _(A1), Q _(B1), Q _(C1))        are obtained from the matrices obtained in step (1) as the real        part (Re) and imaginary part (Im), respectively, of the complex        powers of each phase:

P _(A1) =Re[V _(A1) ·Ī* _(A1) ] Q _(A1) =Im[V _(A1) ·Ī* _(A1)]

P _(B1) =Re[V _(B1) ·Ī* _(B1) ] Q _(B1) =Im[V _(B1) ·Ī* _(B1)]

P _(C1) =Re[V _(C1) ·Ī* _(C1) ] Q _(C1) =Im[V _(C1) ·Ī* _(C1)]

-   -   Step (4): The imbalance power vector (and its various components        (S _(ui), S _(uv)) are obtained from the active and reactive        powers obtained in step (3) as well as from the symmetrical        components obtained in step (2), according to the following        expressions:

${\overset{\_}{S}}_{u} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{1}} \right)} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$${V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)++}}}$$V_{+}{\sqrt{\delta_{u}^{2} + \; \delta_{A}^{2}} \cdot {{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}$${\overset{\_}{S}}_{ui} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{1}} \right)}} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$${V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot \left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)}}$${{\overset{\_}{S}}_{uv} = {V_{+}{\sqrt{\; {\delta_{u}^{2} + {2\; \delta_{A}^{2}}}} \cdot {{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}}}$

-   -   Step (5): Finally, graphic and numerical information about the        imbalance power vector, as well as values of the physical        magnitudes used during the method if desired, is visually        depicted on a suitable display device.

According to the preferred embodiment of the present invention, in step(1) the electrical signals acquired by means of the physical system formeasuring are the instantaneous values of voltage (v_(A), v_(B), v_(C))and intensity (i_(A), i_(B), i_(C)) of the phases (A, B, C) at the pointof the electrical grid where the measurement is being taken. Digitalprocessing in turn consists of separating their components at thefundamental frequency (v_(A1), v_(B1), v_(C1)), (i_(A1), i_(B1),i_(C1)).

According to an additional preferred embodiment of the presentinvention, the method comprises, in addition to or instead of step (5)of displaying described above, a step of emitting an alarm when thecalculated value of at least one of the imbalance power vector (S _(u)),its component S _(ui) and its component S _(uv) exceeds a giventhreshold. The alarm can be of any suitable type in a specificapplication, for example a visual and/or acoustic alarm. The methodthereby warns an operator that a voltage and/or load imbalance that mayhave serious effects on the electrical grid in question is taking placesuch that the operator can take the appropriate measures (for examplecutting off the power supply to that part of the electrical grid) toprotect the circuit and the apparatus connected thereto.

Now turning to FIG. 4 attached hereto, an example of a system formeasuring according to a preferred embodiment of the present inventionis shown. The system comprises voltage and intensity measurement sensors(8) for measuring instantaneous values of voltage and intensity; asignal conditioner (9) for adapting the secondary current of eachmeasurement sensor (8) to the voltage applicable to analog inputs of anacquisition card (10); said acquisition card (10) converting the analogvoltage and intensity signals into a series of discrete samples used asinput in an acquisition module (13); a processing system (11) with amotherboard in which the acquisition card (10) is placed so that thediscrete samples of the voltage and intensity signals can be exchangedwith the acquisition module (13); and a touch screen (12) acting as thedisplay device, connected to a display module (18) for visuallypresenting at least one value calculated by the system for measuring:for example voltages, intensities, active and reactive powers,symmetrical components, imbalance power vector and its components, inmodulus and argument form, in addition to the graphic representationthereof.

In addition, the system for measuring according to the preferredembodiment of the present invention also comprises the followingmodules:

-   -   an acquisition module (13) configured for acquiring the        instantaneous values of voltage (v_(A), v_(B), v_(C)) and        intensity (i_(A), i_(B), i_(C)) of the phases (A, B, C) at a        point of the electrical grid and separating the components        thereof at the fundamental frequency (v_(A1), v_(B1), v_(C1)),        (i_(A1), i_(B1), i_(C1));    -   an analysis module (14) obtaining effective values (V_(A1),        V_(B1), V_(C1)) and arguments (α_(A1), α_(B1), α_(C1)) of the        phase voltages at the fundamental frequency, as well as        effective values (I_(A1), I_(B1), I_(C1)) and arguments (β_(A1),        β_(B1), β_(C1)) of the phase currents at the fundamental        frequency of the electrical grid, from the samples acquired in        the preceding module;    -   a symmetrical module (15) obtaining the effective value        (V₊=V_(A1+)) and the argument (α₊=α_(A1+)) of the positive        sequence voltages and the effective values of the negative        sequence voltage (V⁻=V_(A1−)) and zero sequence voltage        (V₀=V_(A10)) from the results of the preceding module;    -   an active and reactive power module (16) in charge of obtaining        the active power (P_(A1), P_(B1), P_(C1)) and reactive power (Q        _(A1), Q _(B1), Q _(C1)) of each of the phases at the        fundamental frequency for each type of topology of the        electrical installation;    -   an imbalance power vector module (17) in charge of obtaining the        value of the imbalance power vector (S _(u)) and its components,        according to the following equations:

${\overset{\_}{S}}_{u} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{1}} \right)} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$${V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)++}}}$$V_{+}{\sqrt{\delta_{u}^{2} + \; \delta_{A}^{2}} \cdot {{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}$${\overset{\_}{S}}_{ui} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{1}} \right)}} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$${V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot \left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)}}$${\overset{\_}{S}}_{uv} = {V_{+}{\sqrt{\; {\delta_{u}^{2} + {2\; \delta_{A}^{2}}}} \cdot {{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}}$

-   -   a display module (18) in charge of visually depicting on a        screen at least the calculated value of the imbalance power        vector, and optionally its graphic representation and the values        of other physical magnitudes, such as: effective values of        voltages and intensities; active and reactive powers for each        phase; symmetrical components at the fundamental frequency, etc.

According to an additional embodiment of the present invention, thesystem comprises, in addition to or instead of the display module (18),an alarm module configured for emitting an alarm when the calculatedvalue of at least one of the imbalance power vector (S _(u)), itscomponent S _(ui) and its component S _(uv) exceeds a given threshold.As mentioned above, this allows notifying an operator that a voltageand/or load imbalance that may have serious effects on the electricalgrid is taking place so that the operator may take appropriate measuresto protect the circuit and the apparatus connected thereto.

A system for measuring such as the one described herein above ispractically useful in a range of specific applications, such as thefollowing in a non-limiting manner, for example:

-   -   Measuring instruments: The use of a system for measuring        according to the present invention in a measuring instrument        allows separately determining the responsibility pertaining to        users and electric companies in the energies put into play by        the imbalances, as well as accurately measuring the value of        said energies.    -   Protection instruments: Protective relays for receivers and        electrical installations used today to offset excitation voltage        imbalances act by taking into consideration the value of the        degree of imbalance of said voltages (relationship between the        inverse and direct components of the voltages), without taking        into account the magnitude of the energies that emerge due to        said imbalances. The result is that when the degree of imbalance        of the voltages reaches a given value (for example, 2% for one        minute for three-phase electric motors), protective relays used        today open the circuit to protect the receiver or the electrical        installation, even when the energies put into play are not        dangerous. Many receivers and installations therefore stop        working on a number of occasions without this being strictly        necessary, with the subsequent shutdown and reinstatement costs.

By using a system for measuring according to the present invention inprotective relays, it is possible to calculate the energy due to theexclusive effect of voltage imbalances and to evaluate whether dangerousvalues for the receivers and electrical installations are reached, suchthat the opening of the circuit and the subsequent disconnection takesplace only when the imbalance energy may damage said receivers andinstallations, inefficient and untimely openings of the circuits therebybeing prevented.

-   -   Machine regulating equipment: The system for measuring according        to the present invention can be incorporated in an electronic        converter of the type normally used in various regulating        applications, for example in regulating the speed of three-phase        electric motors, controlling DFIG operation in wind turbines,        etc. In wind farms, for example, voltage sags can cause very        undesirable energetic effects, such as disconnection of the        turbines, which is expressly prohibited under the regulations in        force. The technologies that are applied today try to keep wind        turbine operations running throughout the voltage sag by        supplying active energy and reactive energy, without taking the        imbalance energy into account. Therefore, when the sag is very        unbalanced (one-phase and two-phase voltage sags) these        technologies are useless and the turbine must be disconnected to        prevent it from being severely damaged.

The system disclosed herein allows accurately measuring energiescorresponding to voltage imbalances separately from those caused by loadimbalances, therefore providing the information required to act on thecontrol circuit of the DFIG converter, thereby keeping the turbinerunning and minimizing energies caused by imbalances.

-   -   Active filters: Active filters are used in electrical grids to        compensate for the effects of imbalances and harmonic        distortions. Active filters existing on the market do not        distinguish between imbalance and distortion phenomena, given        that they do not allow suitably measuring imbalances. An        imbalance is generally considered to exist when the effective        values of the line currents have a different value in each        phase, even when this difference in values is due to harmonics.        The system for measuring according to the present invention        allows accurately knowing the causes of the imbalances, and        therefore measuring its effects (energies) to effectively        compensate for those imbalances.    -   Electric machine maintenance: According to another embodiment of        the present invention, the system for measuring disclosed herein        is applied to electric machine (transformer and motor)        maintenance. It is thereby possible to detect if a malfunction        of the machine is due to a fault (deterioration of a winding or        busbar, for example), or if, in contrast, it occurs due to        supply voltage imbalances.

Example of Application

To demonstrate the efficacy of the method and system according to thepresent invention and the advantages thereof with respect to the priorart, a comparative study between the imbalance power vector (S _(u),present invention) and the imbalance power phasor (Ā_(u), prior art) wasconducted. The electrical circuit shown in FIG. 5, in which three 100 W,230 V incandescent light bulbs were installed was prepared, firstsupplying them with balanced voltages and then with unbalanced voltages.The supply voltage imbalance was achieved by means of a three-phasephase-variable autotransformer.

A) Balanced Voltages:

The three output (secondary) voltages of the autotransformer wereadjusted to 115.4 V and the active power (P), the reactive power (Q),the imbalance power phasor (A_(u)) and the imbalance power vector(S_(u)) were recorded in a measuring instrument (digital wattmeter). Theresults are shown in Table 1 below.

A) Unbalanced Voltages:

The output (secondary) voltages of the autotransformer were adjusteduntil the following values were reached: Van=100 V, Vbn=100 V andVcn=173.2 V (these voltages have a direct sequence component of 115.4 V,the same value as the balanced voltages in the preceding case). Theobtained results are shown in Table 1 below.

TABLE 1 Power Summary P (W) Q (var) A_(u) (VA) S_(u) (VA) Balancedvoltages 104.29 1.00 0.902 0.902 Unbalanced voltages 129.83 1.32 1.1877.445

From the results shown in Table 1 above, it can be seen that whenbalanced voltages were applied to the light bulbs, the primaryphenomenon was the active power (P) phenomenon. The reactive power (Q)and imbalance powers (A_(u), S_(u)) were negligible. The phasor (A_(u))and the imbalance power vector (S_(u)) were also seen to have the samevery minor values, although they are not quite nil due to the smallimbalance of the light bulbs caused by small differences between them.

It can also be seen that when unbalanced supply voltages were used, theactive power increased by 25.5 W (24.5%) with respect to its value withbalanced voltages, whereas the imbalance power phasor (A_(u)) did notdetect the change (its value is virtually the same with balanced andunbalanced voltages). However, the imbalance power vector (S_(u)) did infact detect the effect of the voltage imbalance, given that it went from0.902 VA to 77.445 VA. This huge increment warns of the increase inactive power consumption caused by the voltage imbalance. This effectcould not have been detected by the imbalance power phasor (A_(u)).

Therefore, the usefulness and the advantages of the method of thepresent invention based on the imbalance power vector (S_(u)) (magnitudeintroduced by the present invention) with respect to the prior art basedon the imbalance power phasor (A_(u)) are demonstrated.

Although the present invention has been described above in reference tospecific embodiments thereof, the skilled person will understand thatmodifications and variations can be made without departing from thescope of the present invention. For example, the skilled person mayconceive of applications in addition to those mentioned hereinabove, inwhich the method and system for measuring electrical imbalances of thepresent invention can be applied.

In addition, although preferred embodiments have been described for boththe method and the system for measuring of the present invention inwhich the value of the imbalance power vector (S _(u)) and that of itscomponents (S _(ui), S _(uv)) are calculated, it must be understood thatonly the imbalance power vector (S _(u)) is calculated in other possibleembodiments of the present invention.

1. A method for measuring imbalances in an electrical grid, comprisingthe steps of: i) obtaining effective values (V_(A1), V_(B1), V_(C1)) andarguments (α_(A1), α_(B1), α_(C1)) of the phase voltages at thefundamental frequency, as well as effective values (I_(A1), I_(B1),I_(C1)) and arguments (β_(A1), β_(B1), β_(C1)) of the phase currents atthe fundamental frequency of the electrical grid; ii) calculating theeffective value (V₊=V_(A1+)) and the argument (α₊=α_(A1+)) of thepositive sequence voltages and the effective values of the negativesequence voltage (V⁻=V_(A1−)) and zero sequence voltage (V₀=V_(A10));iii) determining the active power (P_(A1), P_(B1), P_(C1)) and reactivepower (Q _(A1), Q _(B1), Q _(C1)) of each of the phases at thefundamental frequency from the values of the voltages and currents atthe fundamental frequency; and iv) calculating the value of theimbalance power vector (S _(u)) according to the following equation:${\overset{\_}{S}}_{u} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{1}} \right)} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$${V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)++}}}$$V_{+}{\sqrt{\delta_{u}^{2} + \; \delta_{A}^{2}} \cdot {{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}$wherein a=1∠120°; j is the imaginary unit; δ_(U)=V⁻/V₊ and δ_(A)=V₀/V₊are the degrees of imbalance and asymmetry, respectively, of the phasevoltages; and p, q, z are the orthogonal unit vectors defining the spaceitself of the imbalance power vector.
 2. The method according to claim1, characterized in that it further comprises an initial step ofacquiring instantaneous values of voltage (v_(A), v_(B), v_(C)) andintensity (i_(A), i_(B), i_(C)) of the phases (A, B, C) at a point ofthe electrical grid and separating the components thereof at thefundamental frequency (v_(A1), V_(B1), v_(C1)), (i_(A1), i_(B1),i_(C1)), said values being used in step i) for obtaining the effectivevalues and arguments of the phase voltages and currents at thefundamental frequency of the electrical grid.
 3. The method according toclaim 1, characterized in that it further comprises a step ofcalculating a component (S _(ui)) of the imbalance power vectordetermining the combined effects of voltage and load imbalancesaccording to the following expression:${\overset{\_}{S}}_{ui} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{1}} \right)}} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$$V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot \left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)}$
 4. The methodaccording to claim 1, characterized in that it further comprises a stepof calculating a component (S _(uv)) of the imbalance power vectordetermining the exclusive effect of voltage imbalances according to thefollowing equation:${{{\overset{\_}{S}}_{uv} = {{\quad\quad}V_{+}{\sqrt{\; {\delta_{u}^{2} + {2\; \delta_{A}^{2}}}} \cdot \left. {{\sum\limits_{{x = A},B,C}\; {\left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} +}\quad \right.j\; \frac{P_{x\; 1}}{V_{x\; 1}} \sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {{\quad\quad}\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}}}} \cdot \overset{\_}{z}$5. The method according claim 1, characterized in that it furthercomprises: a step of calculating a component (S _(ui)) of the imbalancepower vector determining the combined effects of voltage and loadimbalances according to the following expression:${\overset{\_}{S}}_{ui} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{1}} \right)}} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$$V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot \left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)}$ a step ofcalculating a component (S _(uv)) of the imbalance power vectordetermining the exclusive effect of voltage imbalances according to thefollowing equation:${{{\overset{\_}{S}}_{uv} =}\quad}{\quad{{\quad\quad}V_{+}{\sqrt{\; {\delta_{u}^{2} + {2\; \delta_{A}^{2}}}} \cdot}}\quad} {{{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}} \sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}$6. The method according to claim 5, characterized in that it furthercomprises a step of visually presenting the calculated value of at leastone of the imbalance power vector (S _(u)), its component S _(ui) andits component S _(uv).
 7. The method according to claim 5, characterizedin that it further comprises a step of emitting an alarm when thecalculated value of at least one of the imbalance power vector (S _(u)),its component S _(ui) and its component S _(uv) exceeds a giventhreshold.
 8. A system for measuring imbalances in an electrical grid,comprising: an analysis module, configured for obtaining effectivevalues (V_(A1), V_(B1), V_(C1)) and arguments (α_(A1), α_(B1), α_(C1))of the phase voltages at the fundamental frequency, as well as effectivevalues (I_(A1), I_(B1), I_(C1)) and arguments (β_(A1), β_(B1), β_(C1))of the phase currents at the fundamental frequency of the electricalgrid; a symmetrical module, configured for obtaining the effective value(V₊=V_(A1+)) and the argument (α₊=α_(A1+)) of the positive sequencevoltages and the effective values of the negative sequence voltage(V⁻=V_(A1−)) and zero sequence voltage (V₀=V_(A10)); an active andreactive power module, configured for obtaining the active power(P_(A1), P_(B1), P_(C1)) and reactive power (Q _(A1), Q _(B1), Q _(C1))of each of the phases at the fundamental frequency; an imbalance powervector module, configured for calculating the value of the imbalancepower vector (S _(u)) according to the following equation:${\overset{\_}{S}}_{u} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{1}} \right)} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$${V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)++}}}$$V_{+}{\sqrt{\delta_{u}^{2} + \; \delta_{A}^{2}} \cdot {{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}$wherein a=1∠120°; j is the imaginary unit; δ_(U)=V⁻/V₊ and δ_(A)=V₀/V₊are the degrees of imbalance and asymmetry, respectively, of the phasevoltages; and p, q, z are the orthogonal unit vectors defining the spaceitself of the imbalance power vector; and an information module,configured for providing information about the calculated value of theimbalance power vector.
 9. The system according to claim 8,characterized in that it further comprises an acquisition moduleconfigured for acquiring the instantaneous values of voltage (v_(A),v_(B), v_(C)) and intensity (i_(A), i_(B), i_(C)) of the phases (A, B,C) at a point of the electrical grid and separating the componentsthereof at the fundamental frequency (v_(A1), v_(B1), v_(C1)), (I_(A1),i_(B1), i_(C1)), said values being used by the analysis module forobtaining the effective values and arguments of the phase voltages andcurrents at the fundamental frequency of the electrical grid.
 10. Thesystem according to claim 8, characterized in that the imbalance powervector module is further configured for calculating a component (S_(ui)) of the imbalance power vector determining the combined effects ofvoltage and load imbalances according to the following expression:${\overset{\_}{S}}_{ui} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{1}} \right)}} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$$V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot \left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)}$
 11. The systemaccording to claim 8, characterized in that the imbalance power vectormodule is further configured for calculating a component (S _(uv)) ofthe imbalance power vector determining the exclusive effect of voltageimbalances according to the following equation:${{{\overset{\_}{S}}_{uv} =}\quad}{\quad{{\quad\quad}V_{+}{\sqrt{\; {\delta_{u}^{2} + {2\; \delta_{A}^{2}}}} \cdot}}\quad} {{{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}} \sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}$12. The system according to claim 8, characterized in that the imbalancepower vector module is further configured for calculating: a component(S _(ui)) of the imbalance power vector determining the combined effectsof voltage and load imbalances according to the following expression:${\overset{\_}{S}}_{ui} = {V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot {\left( {{\begin{matrix}\begin{matrix}{{\frac{P_{A\; 1}}{V_{A\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{A\; 1}} \right)} + {j\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{1}} \right)}} +} \\{{a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\cos \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ {ja}^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\sin \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {a\frac{P_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{{ja}\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{p}} \right)++}}}$$V_{+}{\sqrt{2 + {2\; \delta_{u}^{2}} + {2\; \delta_{A}^{2}}} \cdot \left( {{\begin{matrix}\begin{matrix}{{j\frac{P_{A\; 1}}{V_{A\; 1}}{\sin \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} + {\frac{{\overset{\_}{Q}}_{A\; 1}}{V_{A\; 1}}\; {\cos \left( {\alpha_{+} - \alpha_{A\; 1}} \right)}} +} \\{{j\; a^{2}\frac{P_{B\; 1}}{V_{B\; 1}}\sin \; \left( {\alpha_{+} - \alpha_{B\; 1}} \right)} +}\end{matrix} \\\begin{matrix}{{{+ a^{2}}\frac{{\overset{\_}{Q}}_{B\; 1}}{V_{B\; 1}}{\cos \left( {\alpha_{+} - \alpha_{B\; 1}} \right)}} + {{ja}\frac{P_{C\; 1}}{V_{C\; 1}}{\sin \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}} +} \\{a\frac{{\overset{\_}{Q}}_{C\; 1}}{V_{C\; 1}}{\cos \left( {\alpha_{+} - \alpha_{C\; 1}} \right)}}\end{matrix}\end{matrix} } \cdot \overset{\_}{q}} \right)}$ a component (S_(uv)) of the imbalance power vector determining the exclusive effect ofvoltage imbalances according to the following equation:${{{\overset{\_}{S}}_{uv} =}\quad}{\quad{{\quad\quad}V_{+}{\sqrt{\; {\delta_{u}^{2} + {2\; \delta_{A}^{2}}}} \cdot}}\quad} {{{\sum\limits_{{x = A},B,C}\; \left( {{\frac{P_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}\; {\sin \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}} + {j\; \frac{P_{x\; 1}}{V_{x\; 1}} \sin \; \left( {\alpha_{+} - \alpha_{x\; 1}} \right)} + {\frac{{\overset{\_}{Q}}_{x\; 1}}{V_{x\; 1}}{\cos \left( {\alpha_{+} - \alpha_{x\; 1}} \right)}}} \right)}} \cdot \overset{\_}{z}}$13. The system according to claim 12, characterized in that theinformation module is a display module configured for visually depictingsaid information consisting of at least one of the calculated value andthe graphic representation of said value of at least one of thecalculated value of the imbalance power vector, its component S _(ui)and its component S _(uv).
 14. The system according to claim 12,characterized in that the information module is an alarm moduleconfigured for emitting an alarm when the calculated value of at leastone of the imbalance power vector (S _(u)) its component S _(ui) and itscomponent S _(uv) exceeds a given threshold.
 15. The system according toclaim 8, characterized in that it further comprises: voltage andintensity measurement sensors measuring the instantaneous values ofvoltage and intensity; a signal conditioner for adapting the secondarycurrent of each measurement sensor to the voltage applicable to analoginputs of an acquisition card; an acquisition card converting analogsignals into a series of discrete samples used as input in theacquisition module; a processing system connecting the acquisition cardwith the acquisition module; and a display device connected with thedisplay module for visually presenting at least one value calculated bythe system for measuring.